Systems and methods for ridge selection in scalograms of signals

ABSTRACT

According to embodiments, systems, devices, and methods for ridge selection in scalograms are disclosed. Ridges or ridge components are features within a scalogram which may be computed from a signal such as a physiological (e.g., photoplethysmographic) signal. Ridges may be identified from one or more scalograms of the signal. Parameters characterizing these ridges may be determined. Based at least in part on these parameters, a ridge density distribution function is determined. A ridge is selected from analyzing this ridge density distribution function. In some embodiments, the selected ridge is used to determine a physiological parameter such as respiration rate.

CROSS-REFERENCE TO RELATED APPLICATIONS

This claims the benefit of U.S. Provisional Application Nos. 61/077,029entitled “Systems and Methods for Ridge Selection in Scalograms ofSignals” and 61/077,130 entitled “Systems and Methods of SignalProcessing,” both filed Jun. 30, 2008, which are hereby incorporated byreference herein in their entireties.

SUMMARY

The present disclosure relates to signal processing and, moreparticularly, the present disclosure relates to using continuous wavelettransforms for processing, for example, a photoplethysmograph (PPG)signal.

The present disclosure may be used in connection with any signal havingone or more repetitive components, including, for example, biosignals(e.g., a photoplethysmograph (PPG) signal, electrocardiogram,electroencephalogram, electrogastrogram, electromyogram, heart ratesignals, pathological sounds, ultrasound, or any other suitablebiosignal), dynamic signals, non-destructive testing signals, conditionmonitoring signals, fluid signals, geophysical signals, astronomicalsignals, electrical signals, financial signals including financialindices, sound and speech signals, chemical signals, meteorologicalsignals including climate signals, and/or any other suitable signal,and/or any combination thereof. When one or more scalograms aregenerated from such signals using a continuous wavelet transform,repetitive components of the signals may create one or more ridges at agiven scale. These ridges within the scalograms may be useful inidentifying such repetitive characteristics. For example, scalograms forPPG signals include a ridge at the scale corresponding to a subject'spulse (such ridges are often referred to as the “pulse band”). Somerepetitive characteristics may not form a clean ridge within thescalogram for a variety of reasons. For example, noise may drown-out orbreak-up a repetitive component, or environmental factors (e.g., sensorposition) may affect the quality of the sensed signal. As yet anotherexample, the wavelet employed may accentuate or de-accentuate variouscharacteristics of a signal. One type of wavelet may result in a clearlydefined ridge for the repetitive component, but another may not.

The present disclosure also relates to methods for selecting a ridge ina scalogram of a signal, the method comprising transforming the signalusing a wavelet transform to generate a transformed signal, generating afirst wavelet scalogram based at least in part on the transformedsignal, detecting ridges within a region of the first wavelet scalogram,determining one or more parameters for the detected ridges, determininga ridge density distribution function based at least in part on the oneor more parameters, and selecting a ridge having the scale correspondingto the maximum value of the ridge density distribution function. In someembodiments, the signal is a photoplesthymographic signal. In someembodiments, the method further comprises filtering the first waveletscalogram. Optionally, the method further comprises generating a secondwavelet scalogram based at least in part on a signal derived from thefirst wavelet scalogram and detecting ridges within a region of thesecond wavelet scalogram.

In some embodiments, the parameters of the detected ridges are selectedfrom the group consisting of ridge power, ridge energy, ridge energydensity, ridge amplitude variability, ridge scale variability, ridgeconsistency, intrinsic scale, ridge length, maximum ridge amplitude,standard deviation of intrinsic scale, standard deviation of amplitude,mean scale, median scale, mean amplitude, median amplitude, orstrength-length product. In other embodiments, the method furthercomprises determining a physiological parameter based on the selectedridge. In some embodiments, this physiological parameter is respirationrate.

In some embodiments, ridges may be identified within the scalogramsusing any suitable approach. In some embodiments, the ridges themselvesmay be identified using local maxima. Points not identified as localmaxima may be zeroed out or ignored. The local maxima may be analyzed todetermine, for example, points located with in a predetermined area ofeach other to identify points that make up the ridges. Broken ridges maybe connected by interpolating between adjacent ridges. Broken ridges maybe identified by looking for the end of one ridge that is within apredefined distance/space/area (time, scale, and amplitude) of thebeginning of another ridge. Ridge parameters may be determined in anumber of different ways. In many instances, ridges may be defined by anarray of points, thus allowing for ridge parameterization. Ridges thatfall within certain ranges of scales (e.g., those outside the range ofscales expected to contain the repetitive characteristic) may be ignoredor deleted based on filtering and/or other techniques.

In some embodiments, ridges may be characterized at least in part usingany suitable set of parameters. For example, ridge power, ridge energy,ridge energy density, ridge amplitude variability, ridge scalevariability, ridge consistency, intrinsic scale, ridge length, maximumridge amplitude, standard deviation of intrinsic scale, median scale,median amplitude, strength-length product (e.g., multiplying themaximum, mean, or median strength of all or a portion of a ridge againstthe total length (or any other portion) of the ridge), standarddeviation of amplitude, mean scale, median scale, mean amplitude, medianamplitude, or any other suitable characterizing parameter may bedetermined.

In some embodiments, the computation or derivation of the ridgecharacterizing parameters may be based at least in part on any suitablequantities, e.g., ridge length, maximum amplitude, standard deviation ofthe scale over a predetermined time window, standard deviation of theamplitude at a predetermined scale, mean or median scale, mean or medianamplitude, or a strength-length product, or any other suitablequantities. In some embodiments, the strength-length product is computedby multiplying the maximum strength of a ridge by the length of theridge. In some embodiments, the strength-length product is computed bymultiplying the mean strength of a ridge by the length of the ridge. Inother embodiments, the strength-length product is computed bymultiplying the median strength of a ridge by the length of the ridge.According to some embodiments, the strength-length of a ridge may becomputed using the parameters of the entire ridge or only portionsthereof.

In some embodiments, the ridge density distribution function for one ormore ridges may be determined by a weighted average of the ridgeparameters of these ridges. The ridge density distribution function fora ridge may also be determined from a single ridge parameter, e.g.,strength or strength-length product. The ridge density distributionfunction for one or more ridges may be determined using coefficients andweightings. In some embodiments, ridges may be weighted based at leastin part on the calculated/derived parameters of the ridges. Certainparameters may be considered more important than others in the weightingapplied in a ridge density distribution function. For example, thestrength, length or strength-length of a ridge may be considered a moreimportant parameter than other parameters. Other parameters may decreasethe weighting of a ridge in the ridge density distribution function suchas variability of parameters along the ridge such as amplitude and scalevariation.

In one embodiment, the signal is a PPG signal and the desired,repetitive characteristic is the subject's respiration (for determining,e.g., the subject's respiration rate). One or more scalograms may begenerated from the PPG signal. The one or more scalograms may include,for example, a primary scalogram of the original PPG signal, andsecondary scalograms generated using secondary waveform featuredecoupling (SWFD) applied to the pulse band within the primaryscalogram. Ridges in the scale-range of expected respiration rates(e.g., rates below the pulse ridge) are identified in each of thescalograms. Parameters of these ridges are determined such that ridgepower, energy, energy density, variability, consistency, intrinsicscale, length, or any other suitable characterizing features may becomputed or derived. A ridge density distribution as a function of scaleis calculated, determining the density of ridges as a function of scale,and the optimal scale is selected for determining the respiration rate.The optimal scale may be the scale having the highest ridge densitybased at least in part on the one or more ridge parameters.

The present disclosure also relates to a device for determining aphysiological parameter, the device comprising a sensor for measuring aphysiological signal, and a processor capable of receiving the measuredphysiological signal from the sensor, transforming the signal using awavelet transform to generate a transformed signal, generate a firstwavelet scalogram based at least in part on the transformed signal,detecting ridges within a region of the first wavelet scalogram,determine one or more parameters for the detected ridges, determining aridge density distribution function based at least in part on the one ormore parameters, and selecting a ridge having the scale corresponding tothe maximum value of the ridge density distribution function.Optionally, the device may contain a display for displaying thedetermined physiological parameter.

In an embodiment the disclosure relates to a computer-readable mediumcomprising computer-executable instructions which, when executed by aprocessor, cause the processor to carry out a method for determining aphysiological parameter from one or more scalograms of a signalcomprising transforming the signal using a wavelet transform to generatea transformed signal, generating a first wavelet scalogram based atleast in part on the transformed signal, detecting ridges within aregion of the first wavelet scalogram, determining one or moreparameters for the detected ridges, determining a ridge densitydistribution function based at least in part on the one or moreparameters, and selecting a ridge having the scale corresponding to themaximum value of the ridge density distribution function.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features of the present disclosure, its nature andvarious advantages will be more apparent upon consideration of thefollowing detailed description, taken in conjunction with theaccompanying drawings in which:

FIG. 1 shows an illustrative pulse oximetry system in accordance with anembodiment;

FIG. 2 is a block diagram of the illustrative pulse oximetry system ofFIG. 1 coupled to a patient in accordance with an embodiment;

FIGS. 3( a) and 3(b) show illustrative views of a scalogram derived froma PPG signal in accordance with an embodiment;

FIG. 3( c) shows an illustrative scalogram derived from a signalcontaining two pertinent components in accordance with an embodiment;

FIG. 3( d) shows an illustrative schematic of signals associated with aridge in FIG. 3( c) and illustrative schematics of a further waveletdecomposition of these newly derived signals in accordance with anembodiment;

FIGS. 3( e) and 3(f) are flow charts of illustrative steps involved inperforming an inverse continuous wavelet transform in accordance withembodiments;

FIG. 4 is a block diagram of an illustrative continuous waveletprocessing system in accordance with some embodiments;

FIG. 5 a is a process flow diagram for selecting ridges and determiningrespiration rate according to an embodiment;

FIG. 5 b is a process flow diagram for identifying ridges within one ormore scalograms of a PPG signal according to an embodiment;

FIG. 5 c is a process flow diagram for determining respiration rateusing a ridge density distribution based at least in part on one or moreridge parameters according to an embodiment;

FIG. 6 is an illustration of process 500 of FIGS. 5 a and 5 c on a PPGsignal to determine respiration rate, according to an embodiment;

FIG. 7 shows an exemplary determination of respiration rate according toan embodiment.

FIG. 8 is an illustration of ridges which may be analyzed according toan embodiment;

FIG. 9 is an illustration of weighting of a ridge according to anembodiment; and

FIG. 10 is an illustration of a technique which may be used to creatediscontinuous ridges or “rabbit ears” according to an embodiment.

DETAILED DESCRIPTION

An oximeter is a medical device that may determine the oxygen saturationof the blood. One common type of oximeter is a pulse oximeter, which mayindirectly measure the oxygen saturation of a patients blood (as opposedto measuring oxygen saturation directly by analyzing a blood sampletaken from the patient) and changes in blood volume in the skin.Ancillary to the blood oxygen saturation measurement pulse oximeters mayalso be used to measure the pulse rate of the patient. Pulse oximeterstypically measure and display various blood flow characteristicsincluding, but not limited to, the oxygen saturation of hemoglobin inarterial blood.

An oximeter may include a light sensor that is placed at a site on apatient typically a fingertip, toe, forehead or earlobe, or in the caseof a neonate, across a foot. The oximeter may pass light using a lightsource through blood perfused tissue and photoelectrically sense theabsorption of light in the tissue. For example, the oximeter may measurethe intensity of light that is received at the light sensor as afunction of time. A signal representing light intensity versus time or amathematical manipulation of this signal (e.g., a scaled versionthereof, a log taken thereof a scaled version of a log taken thereof,etc.) may be referred to as the photoplethysmograph (PPG) signal. Inaddition, the term “PPG signal,” as used herein, may also refer to anabsorption signal (i.e., representing the amount of light absorbed bythe tissue) or any suitable mathematical manipulation thereof. The lightintensity or the amount of light absorbed may then be used to calculatethe amount of the blood constituent (e.g., oxyhemoglobin) being measuredas well as the pulse rate and when each individual pulse occurs.

The light passed through the tissue is selected to be of one or morewavelengths that are absorbed by the blood in an amount representativeof the amount of the blood constituent present in the blood. The amountof light passed through the tissue varies in accordance with thechanging amount of blood constituent in the tissue and the related lightabsorption. Red and infrared wavelengths may be used because it has beenobserved that highly oxygenated blood will absorb relatively less redlight and more infrared light than blood with a lower oxygen saturation.By comparing the intensities of two wavelengths at different points inthe pulse cycle, it is possible to estimate the blood oxygen saturationof hemoglobin in arterial blood.

When the measured blood parameter is the oxygen saturation ofhemoglobin, a convenient starting point assumes a saturation calculationbased on Lambert-Beer's law. The following notation will be used herein:

I(λ,t)=I _(o)(λ)exp(−(sβ _(o)(λ)+(1−s)β_(r)(λ))l(t))  (1)

where:λ=wavelength;t=time;I=intensity of light detected;I_(o)=intensity of light transmitted;s=oxygen saturation;β_(o), β_(r)=empirically derived absorption coefficients; andl(t)=a combination of concentration and path length from emitter todetector as a function of time.

The traditional approach measures light absorption at two wavelengths(e.g., red and infrared (IR)), and then calculates saturation by solvingfor the “ratio of ratios” as follows.

1. First, the natural logarithm of (1) is taken (“log” will be used torepresent the natural logarithm) for IR and Red

log I=log I _(o)−(sβ _(o)+(1−s)β_(r))l  (2)

2. (2) is then differentiated with respect to time

$\begin{matrix}{\frac{{\log}\; I}{t} = {{- ( {{s\; \beta_{o}} + {( {1 - s} )\beta_{r}}} )}\frac{I}{t}}} & (3)\end{matrix}$

3. Red (3) is divided by IR (3)

$\begin{matrix}{\frac{{\log}\; {{I( \lambda_{R} )}/{t}}}{{\log}\; {{I( \lambda_{IR} )}/{t}}}\; = \frac{{s\; {\beta_{o}( \lambda_{R} )}} + {( {1 - s} ){\beta_{r}( \lambda_{R} )}}}{{s\; {\beta_{o}( \lambda_{IR} )}} + {( {1 - s} ){\beta_{r}( \lambda_{IR} )}}}} & (4)\end{matrix}$

4. Solving for s

$s = \frac{{\frac{{\log}\; {I( \lambda_{IR} )}}{t}{\beta_{r}( \lambda_{R} )}} - {\frac{{\log}\; {I( \lambda_{R} )}}{t}{\beta_{r}( \lambda_{IR} )}}}{\begin{matrix}{{\frac{{\log}\; {I( \lambda_{R} )}}{t}( {{\beta_{o}( \lambda_{IR} )} - {\beta_{r}( \lambda_{IR} )}} )} -} \\{\frac{{\log}\; {I( \lambda_{IR} )}}{t}( {{\beta_{o}( \lambda_{R} )} - {\beta_{r}( \lambda_{R} )}} )}\end{matrix}}$

Note in discrete time

$\frac{{\log}\; {I( {\lambda,t} )}}{t} \simeq {{\log \; {I( {\lambda,t_{2}} )}} - {\log \; {I( {\lambda,t_{1}} )}}}$

Using log A-log B=log A/B,

$\frac{{\log}\; {I( {\lambda,t} )}}{t} \simeq {\log ( \frac{I( {t_{2},\lambda} )}{I( {t_{1},\lambda} )} )}$

So, (4) can be rewritten as

$\begin{matrix}{{\frac{\frac{{\log}\; {I( \lambda_{R} )}}{t}}{\frac{{\log}\; {I( \lambda_{IR} )}}{t}} \simeq \frac{\log ( \frac{I( {t_{1},\lambda_{R}} )}{I( {t_{2},\lambda_{R}} )} )}{\log ( \frac{I( {t_{1},\lambda_{IR}} )}{I( {t_{2},\lambda_{IR}} )} )}} = R} & (5)\end{matrix}$

where R represents the “ratio of ratios.” Solving (4) for s using (5)gives

$s = {\frac{{\beta_{r}( \lambda_{R} )} - {R\; {\beta_{r}( \lambda_{IR} )}}}{{R( {{\beta_{o}( \lambda_{IR} )} - {\beta_{r}( \lambda_{IR} )}} )} - {\beta_{o}( \lambda_{R} )} + {\beta_{r}( \lambda_{R} )}}.}$

From (5), R can be calculated using two points (e.g., PPG maximum andminimum), or a family of points. One method using a family of pointsuses a modified version of (5). Using the relationship

$\begin{matrix}{\frac{{\log}\; I}{t} = \frac{{I}/{t}}{I}} & (6)\end{matrix}$

now (5) becomes

$\begin{matrix}\begin{matrix}{\frac{\frac{{\log}\; {I( \lambda_{R} )}}{t}}{\frac{{\log}\; {I( \lambda_{IR} )}}{t}} \simeq \frac{\frac{{I( {t_{2},\lambda_{R}} )} - {I( {t_{1},\lambda_{R}} )}}{I( {t_{1},\lambda_{R}} )}}{\frac{{I( {t_{2},\lambda_{IR}} )} - {I( {t_{1},\lambda_{IR}} )}}{I( {t_{1},\lambda_{IR}} )}}} \\{= \frac{\lbrack {{I( {t_{2},\lambda_{R}} )} - {I( {t_{1},\lambda_{R}} )}} \rbrack {I( {t_{1},\lambda_{IR}} )}}{\lbrack {{I( {t_{2},\lambda_{IR}} )} - {I( {t_{1},\lambda_{IR}} )}} \rbrack {I( {t_{1},\lambda_{R}} )}}} \\{= R}\end{matrix} & (7)\end{matrix}$

which defines a cluster of points whose slope of y versus x will give Rwhere

$\begin{matrix}{{{x(t)} = {\lbrack {{I( {t_{2},\lambda_{IR}} )} - {I( {t_{1},\lambda_{IR}} )}} \rbrack {I( {t_{1},\lambda_{R}} )}}}{{y(t)} = {\lbrack {{I( {t_{2},\lambda_{R}} )} - {I( {t_{1},\lambda_{R}} )}} \rbrack {I( {t_{1},\lambda_{IR}} )}}}{{y(t)} = {{{Rx}(t)}.}}} & (8)\end{matrix}$

FIG. 1 is a perspective view of an embodiment of a pulse oximetry system10. System 10 may include a sensor 12 and a pulse oximetry monitor 14.Sensor 12 may include an emitter 16 for emitting light at two or morewavelengths into a patient's tissue. A detector 18 may also be providedin sensor 12 for detecting the light originally from emitter 16 thatemanates from the patient's tissue after passing through the tissue.

According to another embodiment and as will be described, system 10 mayinclude a plurality of sensors forming a sensor array in lieu of singlesensor 12. Each of the sensors of the sensor array may be acomplementary metal oxide semiconductor (CMOS) sensor. Alternatively,each sensor of the array may be charged coupled device (CCD) sensor. Inanother embodiment, the sensor array may be made up of a combination ofCMOS and CCD sensors. The CCD sensor may comprise a photoactive regionand a transmission region for receiving and transmitting data whereasthe CMOS sensor may be made up of an integrated circuit having an arrayof pixel sensors. Each pixel may have a photodetector and an activeamplifier.

According to an embodiment, emitter 16 and detector 18 may be onopposite sides of a digit such as a finger or toe, in which case thelight that is emanating from the tissue has passed completely throughthe digit. In an embodiment, emitter 16 and detector 18 may be arrangedso that light from emitter 16 penetrates the tissue and is reflected bythe tissue into detector 18, such as a sensor designed to obtain pulseoximetry data from a patient's forehead.

In an embodiment, the sensor or sensor array may be connected to anddraw its power from monitor 14 as shown. In another embodiment, thesensor may be wirelessly connected to monitor 14 and include its ownbattery or similar power supply (not shown). Monitor 14 may beconfigured to calculate physiological parameters based at least in parton data received from sensor 12 relating to light emission anddetection. In an alternative embodiment, the calculations may beperformed on the monitoring device itself and the result of the oximetryreading may be passed to monitor 14. Further, monitor 14 may include adisplay 20 configured to display the physiological parameters or otherinformation about the system. In the embodiment shown, monitor 14 mayalso include a speaker 22 to provide an audible sound that may be usedin various other embodiments, such as for example, sounding an audiblealarm in the event that a patient's physiological parameters are notwithin a predefined normal range.

In an embodiment, sensor 12, or the sensor array, may be communicativelycoupled to monitor 14 via a cable 24. However, in other embodiments, awireless transmission device (not shown) or the like may be used insteadof or in addition to cable 24.

In the illustrated embodiment, pulse oximetry system 10 may also includea multi-parameter patient monitor 26. The monitor may be cathode raytube type, a flat panel display (as shown) such as a liquid crystaldisplay (LCD) or a plasma display, or any other type of monitor nowknown or later developed. Multi-parameter patient monitor 26 may beconfigured to calculate physiological parameters and to provide adisplay 28 for information from monitor 14 and from other medicalmonitoring devices or systems (not shown). For example, multiparameterpatient monitor 26 may be configured to display an estimate of apatient's blood oxygen saturation generated by pulse oximetry monitor 14(referred to as an “SpO₂” measurement), pulse rate information frommonitor 14 and blood pressure from a blood pressure monitor (not shown)on display 28.

Monitor 14 may be communicatively coupled to multi-parameter patientmonitor 26 via a cable 32 or 34 that is coupled to a sensor input portor a digital communications port, respectively and/or may communicatewirelessly (not shown). In addition, monitor 14 and/or multi-parameterpatient monitor 26 may be coupled to a network to enable the sharing ofinformation with servers or other workstations (not shown). Monitor 14may be powered by a battery (not shown) or by a conventional powersource such as a wall outlet.

FIG. 2 is a block diagram of a pulse oximetry system, such as pulseoximetry system 10 of FIG. 1, which may be coupled to a patient 40 inaccordance with an embodiment. Certain illustrative components of sensor12 and monitor 14 are illustrated in FIG. 2. Sensor 12 may includeemitter 16, detector 18, and encoder 42. In the embodiment shown,emitter 16 may be configured to emit at least two wavelengths of light(e.g., RED and IR) into a patient's tissue 40. Hence, emitter 16 mayinclude a RED light emitting light source such as RED light emittingdiode (LED) 44 and an IR light emitting light source such as IR LED 46for emitting light into the patient's tissue 40 at the wavelengths usedto calculate the patient's physiological parameters. In one embodiment,the RED wavelength may be between about 600 nm and about 700 nm, and theIR wavelength may be between about 800 nm and about 1000 nm. Inembodiments where a sensor array is used in place of single sensor, eachsensor may be configured to emit a single wavelength. For example, afirst sensor emits only a RED light while a second only emits an IRlight.

It will be understood that as used herein, the term “light” may refer toenergy produced by radiative sources and may include one or more ofultrasound, radio, microwave, millimeter wave, infrared, visible,ultraviolet, gamma ray or X-ray electromagnetic radiation. As usedherein, light may also include any wavelength within the radio,microwave, infrared, visible, ultraviolet, or X-ray spectra, and thatany suitable wavelength of electromagnetic radiation may be appropriatefor use with the present techniques. Detector 18 may be chosen to bespecifically sensitive to the chosen targeted energy spectrum of theemitter 16.

In an embodiment, detector 18 may be configured to detect the intensityof light at the RED and IR wavelengths. Alternatively, each sensor inthe array may be configured to detect an intensity of a singlewavelength. In operation, light may enter detector 18 after passingthrough the patient's tissue 40. Detector 18 may convert the intensityof the received light into an electrical signal. The light intensity isdirectly related to the absorbance and/or reflectance of light in thetissue 40. That is, when more light at a certain wavelength is absorbedor reflected, less light of that wavelength is received from the tissueby the detector 18. After converting the received light to an electricalsignal, detector 18 may send the signal to monitor 14, wherephysiological parameters may be calculated based on the absorption ofthe RED and IR wavelengths in the patient's tissue 40.

In an embodiment, encoder 42 may contain information about sensor 12,such as what type of sensor it is (e.g., whether the sensor is intendedfor placement on a forehead or digit) and the wavelengths of lightemitted by emitter 16. This information may be used by monitor 14 toselect appropriate algorithms, lookup tables and/or calibrationcoefficients stored in monitor 14 for calculating the patient'sphysiological parameters.

Encoder 42 may contain information specific to patient 40, such as, forexample, the patient's age, weight, and diagnosis. This information mayallow monitor 14 to determine, for example, patient-specific thresholdranges in which the patient's physiological parameter measurementsshould fall and to enable or disable additional physiological parameteralgorithms. Encoder 42 may, for instance, be a coded resistor whichstores values corresponding to the type of sensor 12 or the type of eachsensor in the sensor array, the wavelengths of light emitted by emitter16 on each sensor of the sensor array, and/or the patient'scharacteristics. In another embodiment, encoder 42 may include a memoryon which one or more of the following information may be stored forcommunication to monitor 14: the type of the sensor 12; the wavelengthsof light emitted by emitter 16; the particular wavelength each sensor inthe sensor array is monitoring; a signal threshold for each sensor inthe sensor array; any other suitable information; or any combinationthereof.

In an embodiment, signals from detector 18 and encoder 42 may betransmitted to monitor 14. In the embodiment shown, monitor 14 mayinclude a general-purpose microprocessor 48 connected to an internal bus50. Microprocessor 48 may be adapted to execute software, which mayinclude an operating system and one or more applications, as part ofperforming the functions described herein. Also connected to bus 50 maybe a read-only memory (ROM) 52, a random access memory (RAM) 54, userinputs 56, display 20, and speaker 22.

RAM 54 and ROM 52 are illustrated by way of example, and not limitation.Any suitable computer-readable media may be used in the system for datastorage. Computer-readable media are capable of storing information thatcan be interpreted by microprocessor 48. This information may be data ormay take the form of computer-executable instructions, such as softwareapplications, that cause the microprocessor to perform certain functionsand/or computer-implemented methods. Depending on the embodiment, suchcomputer-readable media may include computer storage media andcommunication media. Computer storage media may include volatile andnon-volatile, removable and non-removable media implemented in anymethod or technology for storage of information such ascomputer-readable instructions, data structures, program modules orother data. Computer storage media may include, but is not limited to,RAM, ROM, EPROM, EEPROM, flash memory or other solid state memorytechnology, CD-ROM, DVD, or other optical storage, magnetic cassettes,magnetic tape, magnetic disk storage or other magnetic storage devices,or any other medium which can be used to store the desired informationand which can be accessed by components of the system.

In the embodiment shown, a time processing unit (TPU) 58 may providetiming control signals to a light drive circuitry 60, which may controlwhen emitter 16 is illuminated and multiplexed timing for the RED LED 44and the IR LED 46. TPU 58 may also control the gating-in of signals fromdetector 18 through an amplifier 62 and a switching circuit 64. Thesesignals are sampled at the proper time, depending upon which lightsource is illuminated. The received signal from detector 18 may bepassed through an amplifier 66, a low pass filter 68, and ananalog-to-digital converter 70. The digital data may then be stored in aqueued serial module (QSM) 72 (or buffer) for later downloading to RAM54 as QSM 72 fills up. In one embodiment, there may be multiple separateparallel paths having amplifier 66, filter 68, and A/D converter 70 formultiple light wavelengths or spectra received.

In an embodiment, microprocessor 48 may determine the patient'sphysiological parameters, such as SpO₂ and pulse rate, using variousalgorithms and/or look-up tables based on the value of the receivedsignals and/or data corresponding to the light received by detector 18.Signals corresponding to information about patient 40, and particularlyabout the intensity of light emanating from a patient's tissue overtime, may be transmitted from encoder 42 to a decoder 74. These signalsmay include, for example, encoded information relating to patientcharacteristics. Decoder 74 may translate these signals to enable themicroprocessor to determine the thresholds based on algorithms or lookuptables stored in ROM 52. User inputs 56 may be used to enter informationabout the patient, such as age, weight, height, diagnosis, medications,treatments, and so forth. In an embodiment, display 20 may exhibit alist of values which may generally apply to the patient, such as, forexample, age ranges or medication families, which the user may selectusing user inputs 56.

The optical signal through the tissue can be degraded by noise, amongother sources. One source of noise is ambient light that reaches thelight detector. Another source of noise is electromagnetic coupling fromother electronic instruments. Movement of the patient also introducesnoise and affects the signal. For example, the contact between thedetector and the skin, or the emitter and the skin, can be temporarilydisrupted when movement causes either to move away from the skin. Inaddition, because blood is a fluid, it responds differently than thesurrounding tissue to inertial effects, thus resulting in momentarychanges in volume at the point to which the oximeter probe is attached.

Noise (e.g., from patient movement) can degrade a pulse oximetry signalrelied upon by a physician, without the physician's awareness. This isespecially true if the monitoring of the patient is remote, the motionis too small to be observed, or the doctor is watching the instrument orother parts of the patient, and not the sensor site. Processing pulseoximetry (i.e., PPG) signals may involve operations that reduce theamount of noise present in the signals or otherwise identify noisecomponents in order to prevent them from affecting measurements ofphysiological parameters derived from the PPG signals.

It will be understood that the present disclosure is applicable to anysuitable signals and that PPG signals are used merely for illustrativepurposes. Those skilled in the art will recognize that the presentdisclosure has wide applicability to other signals including, but notlimited to other biosignals (e.g., electrocardiogram,electroencephalogram, electrogastrogram, electromyogram, heart ratesignals, pathological sounds, ultrasound, or any other suitablebiosignal), dynamic signals, non-destructive testing signals, conditionmonitoring signals, fluid signals, geophysical signals, astronomicalsignals, electrical signals, financial signals including financialindices, sound and speech signals, chemical signals, meteorologicalsignals including climate signals, and/or any other suitable signal,and/or any combination thereof.

In one embodiment, a PPG signal may be transformed using a continuouswavelet transform. Information derived from the transform of the PPGsignal (i.e., in wavelet space) may be used to provide measurements ofone or more physiological parameters.

The continuous wavelet transform of a signal x(t) in accordance with thepresent disclosure may be defined as

$\begin{matrix}{{T( {a,b} )} = {\frac{1}{\sqrt{a}}{\int_{- \infty}^{+ \infty}{{x(t)}{\psi^{*}( \frac{t - b}{a} )}\ {t}}}}} & (9)\end{matrix}$

where ψ*(t) is the complex conjugate of the wavelet function ψ(t), a isthe dilation parameter of the wavelet and b is the location parameter ofthe wavelet. The transform given by equation (9) may be used toconstruct a representation of a signal on a transform surface. Thetransform may be regarded as a time-scale representation. Wavelets arecomposed of a range of frequencies, one of which may be denoted as thecharacteristic frequency of the wavelet, where the characteristicfrequency associated with the wavelet is inversely proportional to thescale a. One example of a characteristic frequency is the dominantfrequency. Each scale of a particular wavelet may have a differentcharacteristic frequency. The underlying mathematical detail requiredfor the implementation within a time-scale can be found, for example, inPaul S. Addison, The Illustrated Wavelet Transform Handbook (Taylor &Francis Group 2002), which is hereby incorporated by reference herein inits entirety.

The continuous wavelet transform decomposes a signal using wavelets,which are generally highly localized in time. The continuous wavelettransform may provide a higher resolution relative to discretetransforms, thus providing the ability to garner more information fromsignals than typical frequency transforms such as Fourier transforms (orany other spectral techniques) or discrete wavelet transforms.Continuous wavelet transforms allow for the use of a range of waveletswith scales spanning the scales of interest of a signal such that smallscale signal components correlate well with the smaller scale waveletsand thus manifest at high energies at smaller scales in the transform.Likewise, large scale signal components correlate well with the largerscale wavelets and thus manifest at high energies at larger scales inthe transform. Thus, components at different scales may be separated andextracted in the wavelet transform domain. Moreover, the use of acontinuous range of wavelets in scale and time position allows for ahigher resolution transform than is possible relative to discretetechniques.

In addition, transforms and operations that convert a signal or anyother type of data into a spectral (i.e., frequency) domain necessarilycreate a series of frequency transform values in a two-dimensionalcoordinate system where the two dimensions may be frequency and, forexample, amplitude. For example, any type of Fourier transform wouldgenerate such a two-dimensional spectrum. In contrast, wavelettransforms, such as continuous wavelet transforms, are required to bedefined in a three-dimensional coordinate system and generate a surfacewith dimensions of time, scale and, for example, amplitude. Hence,operations performed in a spectral domain cannot be performed in thewavelet domain; instead the wavelet surface must be transformed into aspectrum (i.e., by performing an inverse wavelet transform to convertthe wavelet surface into the time domain and then performing a spectraltransform from the time domain). Conversely, operations performed in thewavelet domain cannot be performed in the spectral domain; instead aspectrum must first be transformed into a wavelet surface (i.e. byperforming an inverse spectral transform to convert the spectral domaininto the time domain and then performing a wavelet transform from thetime domain). Nor does a cross-section of the three-dimensional waveletsurface along, for example, a particular point in time equate to afrequency spectrum upon which spectral-based techniques may be used. Atleast because wavelet space includes a time dimension, spectraltechniques and wavelet techniques are not interchangeable. It will beunderstood that converting a system that relies on spectral domainprocessing to one that relies on wavelet space processing would requiresignificant and fundamental modifications to the system in order toaccommodate the wavelet space processing (e.g., to derive arepresentative energy value for a signal or part of a signal requiresintegrating twice, across time and scale, in the wavelet domain while,conversely, one integration across frequency is required to derive arepresentative energy value from a spectral domain). As a furtherexample, to reconstruct a temporal signal requires integrating twice,across time and scale, in the wavelet domain while, conversely, oneintegration across frequency is required to derive a temporal signalfrom a spectral domain. It is well known in the art that, in addition toor as an alternative to amplitude, parameters such as energy density,modulus, phase, among others may all be generated using such transformsand that these parameters have distinctly different contexts andmeanings when defined in a two-dimensional frequency coordinate systemrather than a three-dimensional wavelet coordinate system. For example,the phase of a Fourier system is calculated with respect to a singleorigin for all frequencies while the phase for a wavelet system isunfolded into two dimensions with respect to a wavelet's location (oftenin time) and scale.

The energy density function of the wavelet transform, the scalogram, isdefined as

S(a,b)=|T(a,b)|²  (10)

where ‘∥’ is the modulus operator. The scalogram may be resealed foruseful purposes. One common resealing is defined as

$\begin{matrix}{{S_{R}( {a,b} )} = \frac{{{T( {a,b} )}}^{2}}{a}} & (11)\end{matrix}$

and is useful for defining ridges in wavelet space when, for example,the Morlet wavelet is used. Ridges are defined as the locus of points oflocal maxima in the plane Any reasonable definition of a ridge may beemployed in the method. Also included as a definition of a ridge hereinare paths displaced from the locus of the local maxima. A ridgeassociated with only the locus of points of local maxima in the planeare labeled a “maxima ridge”.

For implementations requiring fast numerical computation, the wavelettransform may be expressed as an approximation using Fourier transforms.Pursuant to the convolution theorem, because the wavelet transform isthe cross-correlation of the signal with the wavelet function, thewavelet transform may be approximated in terms of an inverse FFT of theproduct of the Fourier transform of the signal and the Fourier transformof the wavelet for each required a scale and then multiplying the resultby √{square root over (a)}.

In the discussion of the technology which follows herein, the“scalogram” may be taken to include all suitable forms of rescalingincluding, but not limited to, the original unsealed waveletrepresentation, linear resealing, any power of the modulus of thewavelet transform, or any other suitable resealing. In addition, forpurposes of clarity and conciseness, the term “scalogram” shall be takento mean the wavelet transform, T(a,b) itself, or any part thereof. Forexample, the real part of the wavelet transform, the imaginary part ofthe wavelet transform, the phase of the wavelet transform, any othersuitable part of the wavelet transform, or any combination thereof isintended to be conveyed by the term “scalogram”.

A scale, which may be interpreted as a representative temporal period,may be converted to a characteristic frequency of the wavelet function.The characteristic frequency associated with a wavelet of arbitrary ascale is given by

$\begin{matrix}{f = \frac{f_{c}}{a}} & (12)\end{matrix}$

where f_(c), the characteristic frequency of the mother wavelet (i.e.,at a=1), becomes a scaling constant and f is the representative orcharacteristic frequency for the wavelet at arbitrary scale a.

Any suitable wavelet function may be used in connection with the presentdisclosure. One of the most commonly used complex wavelets, the Morletwavelet, is defined as:

ψ(t)=π^(−1/4)(e ^(12πf) ⁰ ^(t) ⇄e ^(−(2πf) ⁰ ⁾ ² ^(/2))e ^(−t) ²^(/2)  (13)

where f₀ is the central frequency of the mother wavelet. The second termin the parenthesis is known as the correction term, as it corrects forthe non-zero mean of the complex sinusoid within the Gaussian window. Inpractice, it becomes negligible for values of f₀>>0 and can be ignored,in which case, the Morlet wavelet can be written in a simpler form as

$\begin{matrix}{{\psi (t)} = {\frac{1}{\pi^{1/4}}^{\; 2\pi \; f_{0}t}^{{- t^{2}}/2}}} & (14)\end{matrix}$

This wavelet is a complex wave within a scaled Gaussian envelope. Whileboth definitions of the Morlet wavelet are included herein, the functionof equation (14) is not strictly a wavelet as it has a non-zero mean(i.e., the zero frequency term of its corresponding energy spectrum isnon-zero). However, it will be recognized by those skilled in the artthat equation (14) may be used in practice with f₀>>0 with minimal errorand is included (as well as other similar near wavelet functions) in thedefinition of a wavelet herein. A more detailed overview of theunderlying wavelet theory, including the definition of a waveletfunction, can be found in the general literature. Discussed herein ishow wavelet transform features may be extracted from the waveletdecomposition of signals. For example, wavelet decomposition of PPGsignals may be used to provide clinically useful information within amedical device.

Pertinent repeating features in a signal give rise to a time-scale bandin wavelet space or a rescaled wavelet space. For example, the pulsecomponent of a PPG signal produces a dominant band in wavelet space ator around the pulse frequency. FIGS. 3( a) and (b) show two views of anillustrative scalogram derived from a PPG signal, according to anembodiment. The figures show an example of the band caused by the pulsecomponent in such a signal. The pulse band is located between the dashedlines in the plot of FIG. 3( a). The band is formed from a series ofdominant coalescing features across the scalogram. This can be clearlyseen as a raised band across the transform surface in FIG. 3( b) locatedwithin the region of scales indicated by the arrow in the plot(corresponding to 60 beats per minute). The maxima of this band withrespect to scale is the ridge. The locus of the ridge is shown as ablack curve on top of the band in FIG. 3( b). By employing a suitablerescaling of the scalogram, such as that given in equation (11), theridges found in wavelet space may be related to the instantaneousfrequency of the signal. In this way, the pulse rate may be obtainedfrom the PPG signal. Instead of resealing the scalogram, a suitablepredefined relationship between the scale obtained from the ridge on thewavelet surface and the actual pulse rate may also be used to determinethe pulse rate.

By mapping the time-scale coordinates of the pulse ridge onto thewavelet phase information gained through the wavelet transform,individual pulses may be captured. In this way, both times betweenindividual pulses and the timing of components within each pulse may bemonitored and used to detect heart beat anomalies, measure arterialsystem compliance, or perform any other suitable calculations ordiagnostics. Alternative definitions of a ridge may be employed.Alternative relationships between the ridge and the pulse frequency ofoccurrence may be employed.

As discussed above, pertinent repeating features in the signal give riseto a time-scale band in wavelet space or a resealed wavelet space. For aperiodic signal, this band remains at a constant scale in the time-scaleplane. For many real signals, especially biological signals, the bandmay be non-stationary; varying in scale, amplitude, or both over time.FIG. 3( c) shows an illustrative schematic of a wavelet transform of asignal containing two pertinent components leading to two bands in thetransform space, according to an embodiment. These bands are labeledband A and band B on the three-dimensional schematic of the waveletsurface. In this embodiment, the band ridge is defined as the locus ofthe peak values of these bands with respect to scale. For purposes ofdiscussion, it may be assumed that band B contains the signalinformation of interest. This will be referred to as the “primary band”.In addition, it may be assumed that the system from which the signaloriginates, and from which the transform is subsequently derived,exhibits some form of coupling between the signal components in band Aand band B. When noise or other erroneous features are present in thesignal with similar spectral characteristics of the features of band Bthen the information within band B can become ambiguous (i.e., obscured,fragmented or missing). In this case, the ridge of band A may befollowed in wavelet space and extracted either as an amplitude signal ora scale signal which will be referred to as the “ridge amplitudeperturbation” (RAP) signal and the “ridge scale perturbation” (RSP)signal, respectively. The RAP and RSP signals may be extracted byprojecting the ridge onto the time-amplitude or time-scale planes,respectively. The top plots of FIG. 3( d) show a schematic of the RAPand RSP signals associated with ridge A in FIG. 3( c). Below these RAPand RSP signals are schematics of a further wavelet decomposition ofthese newly derived signals. This secondary wavelet decomposition allowsfor information in the region of band B in FIG. 3( c) to be madeavailable as band C and band D. The ridges of bands C and D may serve asinstantaneous time-scale characteristic measures of the signalcomponents causing bands C and D. This technique, which will be referredto herein as secondary wavelet feature decoupling (SWFD), may allowinformation concerning the nature of the signal components associatedwith the underlying physical process causing the primary band B (FIG. 3(c)) to be extracted when band B itself is obscured in the presence ofnoise or other erroneous signal features.

In some instances, an inverse continuous wavelet transform may bedesired, such as when modifications to a scalogram (or modifications tothe coefficients of a transformed signal) have been made in order to,for example, remove artifacts. In one embodiment, there is an inversecontinuous wavelet transform which allows the original signal to berecovered from its wavelet transform by integrating over all scales andlocations, a and b:

$\begin{matrix}{{x(t)} = {\frac{1}{C_{g}}{\int_{- \infty}^{\infty}{\int_{0}^{\infty}{{T( {a,b} )}\frac{1}{\sqrt{a}}{\psi ( \frac{t - b}{a} )}\ \frac{{a}\ {b}}{a^{2}}}}}}} & (15)\end{matrix}$

which may also be written as:

$\begin{matrix}{{x(t)} = {\frac{1}{C_{g}}{\int_{- \infty}^{\infty}{\int_{0}^{\infty}{{T( {a,b} )}{\psi_{a,b}(t)}\ \frac{{a}\ {b}}{a^{2}}}}}}} & (16)\end{matrix}$

where C_(g) is a scalar value known as the admissibility constant. It iswavelet type dependent and may be calculated from:

$\begin{matrix}{C_{g} = {\int_{0}^{\infty}{\frac{{{\hat{\psi}(f)}}^{2}}{f}\ {f}}}} & (17)\end{matrix}$

FIG. 3( e) is a flow chart of illustrative steps that may be taken toperform an inverse continuous wavelet transform in accordance with theabove discussion. An approximation to the inverse transform may be madeby considering equation (15) to be a series of convolutions acrossscales. It shall be understood that there is no complex conjugate here,unlike for the cross correlations of the forward transform. As well asintegrating over all of a and b for each time t, this equation may alsotake advantage of the convolution theorem which allows the inversewavelet transform to be executed using a series of multiplications. FIG.3( f) is a flow chart of illustrative steps that may be taken to performan approximation of an inverse continuous wavelet transform. It will beunderstood that any other suitable technique for performing an inversecontinuous wavelet transform may be used in accordance with the presentdisclosure.

FIG. 4 is an illustrative continuous wavelet processing system inaccordance with an embodiment. In this embodiment, input signalgenerator 410 generates an input signal 416. As illustrated, inputsignal generator 410 may include oximeter 420 coupled to sensor 418,which may provide as input signal 416, a PPG signal. It will beunderstood that input signal generator 410 may include any suitablesignal source, signal generating data, signal generating equipment, orany combination thereof to produce signal 416. Signal 416 may be anysuitable signal or signals, such as, for example, biosignals (e.g.,electrocardiogram, electroencephalogram, electrogastrogram,electromyogram, heart rate signals, pathological sounds, ultrasound, orany other suitable biosignal), dynamic signals, non-destructive testingsignals, condition monitoring signals, fluid signals, geophysicalsignals, astronomical signals, electrical signals, financial signalsincluding financial indices, sound and speech signals, chemical signals,meteorological signals including climate signals, and/or any othersuitable signal, and/or any combination thereof.

In this embodiment, signal 416 may be coupled to processor 412.Processor 412 may be any suitable software, firmware, and/or hardware,and/or combinations thereof for processing signal 416. For example,processor 412 may include one or more hardware processors (e.g.,integrated circuits), one or more software modules, computer-readablemedia such as memory, firmware, or any combination thereof. Processor412 may, for example, be a computer or may be one or more chips (i.e.,integrated circuits). Processor 412 may perform the calculationsassociated with the continuous wavelet transforms of the presentdisclosure as well as the calculations associated with any suitableinterrogations of the transforms. Processor 412 may perform any suitablesignal processing of signal 416 to filter signal 416, such as anysuitable band-pass filtering, adaptive filtering, closed-loop filtering,and/or any other suitable filtering, and/or any combination thereof.

Processor 412 may be coupled to one or more memory devices (not shown)or incorporate one or more memory devices such as any suitable volatilememory device (e.g., RAM, registers, etc.), non-volatile memory device(e.g., ROM, EPROM, magnetic storage device, optical storage device,flash memory, etc.), or both, The memory may be used by processor 412to, for example, store data corresponding to a continuous wavelettransform of input signal 416, such as data representing a scalogram. Inone embodiment, data representing a scalogram may be stored in RAM ormemory internal to processor 412 as any suitable three-dimensional datastructure such as a three-dimensional array that represents thescalogram as energy levels in a time-scale plane. Any other suitabledata structure may be used to store data representing a scalogram.

Processor 412 may be coupled to output 414. Output 414 may be anysuitable output device such as, for example, one or more medical devices(e.g., a medical monitor that displays various physiological parameters,a medical alarm, or any other suitable medical device that eitherdisplays physiological parameters or uses the output of processor 412 asan input), one or more display devices (e.g., monitor, PDA, mobilephone, any other suitable display device, or any combination thereof),one or more audio devices, one or more memory devices (e.g., hard diskdrive, flash memory, RAM, optical disk, any other suitable memorydevice, or any combination thereof), one or more printing devices, anyother suitable output device, or any combination thereof.

It will be understood that system 400 may be incorporated into system 10(FIGS. 1 and 2) in which, for example, input signal generator 410 may beimplemented as parts of sensor 12 and monitor 14 and processor 412 maybe implemented as part of monitor 14.

Embodiments will now be discussed in connection with FIGS. 5 through 10.In particular; systems and methods for ridge selection and determinationrespiration rate from one or more scalograms of a PPG signal will bediscussed in detail. FIGS. 5 a-c illustrate processes involved inselecting ridges and determining respiration rate from a PPG signal,while FIGS. 6 and 7 are illustrative embodiments of the processesdescribed in FIGS. 5 a-c. FIGS. 8-10 are more detailed illustrations ofridges in scalograms, and of exemplary ridge parameterizations.

FIGS. 5 a-5 c illustrate process flow diagrams for a method forselecting ridges and determining a physiological parameter, e.g.,respiration rate, according to an embodiment. FIG. 5 a shows process 500for a signal 501 which may be executed on processor 412 of waveletprocessing system 400 in FIG. 4. FIGS. 5 b and 5 c show process flowdiagrams for determining respiration rate from a PPG signal, includingthe processes of identifying ridges, calculating ridge parameters, anddetermining a ridge density distribution function based on thedetermined ridge parameters, which may be executed on processor 412 ofwavelet processing system 400 in FIG. 4.

In FIG. 5 a, a physiological signal is received (step 501) from, e.g., asensor such as oximeter 420 in FIG. 4, and transformed by applying acontinuous wavelet transform to generate one or more primary scalograms(step 504). Primary scalograms may encompass any scalogram computedusing the sensed signal 501, i.e., scalograms offset in time or offsetin scale are also considered primary scalograms. As discussed above,pertinent repeating features in the signal may give rise to a time-scaleband in wavelet space or in resealed wavelet space in the primaryscalograms 504, or the secondary scalograms 506. In many real signals,e.g., PPG signals, these bands may be non-stationary; varying in scale,amplitude, or both over time. Optionally, secondary scalograms may bealso be generated (step 506). These secondary scalograms may begenerated based in part on the primary scalograms, e.g., based on aSFWD, and the signal. Ridges may then be identified or detected (step507) and one or more ridge parameters for each identified ridge may bedetermined (step 511). Based on the determined ridge parameters, a ridgedensity distribution (RDD) function is determined (step 512). The scalecorresponding to the maximum value of the RDD function is selected (step514), and this scale is the output physiological parameter (step 516).These steps will now be described in relation to a PPG signal in theprocess flow diagrams of FIGS. 5 b and 5 c.

FIG. 5 b illustrates a process flow diagram for a method for identifyingprimary and/or secondary ridges from a PPG signal, according to anembodiment. Physiological signal 502, e.g., a PPG signal, may bereceived from oximeter 420 by processor 412 of FIG. 4. In step 503, thePPG signal is pre-processed, for example, to remove noise artifacts orunwanted modulation effects. Processor 412 of FIG. 4 may compute thewavelet transform such as a continuous wavelet transform of signal 502to obtain the primary scalogram(s) 504 of signal 502, generatedaccording to the discussion relating to FIGS. 3( a) to 3(e) above (step503). This primary scalogram may contain ridges in the pulse scale-rangeor the respiration scale-range, or in any other scale-range. Forinstance, the primary scalogram may contain ridges corresponding to,among others, the pulse ridge in the pulse scale-range, e.g., 1 Hz, andthe respiration ridge in the respiration scale-range, e.g., 0.3 Hz. Insome embodiments, only the primary scalogram is used to identify ordetect ridges. The primary scalograms 504 of the signal may be filteredusing filter 1 508 to remove undesired portions of the scalograms, e.g.,noise artifacts or pulse ridges. Optionally, in other embodiments, theprimary scalograms may be used to compute one or more secondaryscalograms 506 after the pulse ridge loci are extracted (step 509).These secondary scalograms may be filtered using filter 2 510 to removeundesired portions of the scalograms, e.g., the pulse ridge or pulseband. The secondary scalograms may be based on any suitable mapping ofthe primary scalogram, e.g., SWFD, that results in a secondary signal(step 518). Examples of SWFDs include a signal that is obtained from atime-scale mapping along the extracted pulse ridge loci (illustrated inGraph 608 as will be explained below in relation to FIG. 6), alsoreferred to as an S-mapping or S component or the Scale Modulation (SM)ridge component, which is an example of an RSP signal, a time-energy ortime-scalogram amplitude mapping along the extracted pulse ridge loci(illustrated in Graph 610 as will be explained in relation to FIG. 6),also known as an A-mapping or A component or the Amplitude Modulation(AM) ridge component, or a time-energy or time-scalogram amplitudemapping at a locus of points equally offset from the extracted pulseridge loci (illustrated in Graph 612 as will be explained in relation toFIG. 6), also known as an O-mapping or O component Continuous wavelettransforms of the O-mapping, S-mapping, and A-mapping, may be computed(step 506), and these transforms are referred to as secondaryscalograms. These secondary scalograms may contain ridge componentscorresponding to the respiration scale-range. Although the secondaryscalograms are discussed as corresponding to the A-mapping, S-mapping,and O-mapping, any other suitable secondary scalogram may be used. Notethat the primary and secondary scalograms can be computed using apredetermined time period within the signal 504 and the primaryscalograms 504, e.g., a five-second time period or any other suitabletime period. In some embodiments, a moving time period or window may beused to perform the scalogram computations. The secondary scalograms maybe filtered, for example, to remove noise or unwanted components, withfilter 2 510 (or a second wavelet scalogram mask).

Once the primary, and in some embodiments, secondary scalograms, havebeen computed, processor 412 of FIG. 4 may detect and identify ridgeswithin these scalograms in the respiration scale-range (steps 513 and/or515). Such an identification or detection may be performed by selectingridges that are within an acceptable breath frequency, e.g. 12-18breaths per minute, or 0.2-0.3 Hz. Any suitable identification methodmay be used to select ridges within the respiration scale range. Theoutput of the identification process are a set of primary scalogramridges 520, and a set of secondary scalogram ridges 522.

FIG. 5 c illustrates a process flow diagram for determining respirationrate from the set of primary scalogram ridges 520, and a set ofsecondary scalogram ridges 522 in FIG. 5 b, according to an embodiment.In particular, FIG. 5 c is a process flow diagram 550 for calculatingand deriving a ridge density distribution from the primary and/orsecondary scalogram ridges based on the selected ridge parameters. Inone embodiment, the primary scalogram ridges 520 are parameterized,i.e., parameters that characterize these ridges are calculated and/orderived. Optionally, in other embodiments, both the primary scalogramridges 520 and the secondary scalogram ridges 522 are parameterized(step 524). Examples of such parameters include ridge strength, ridgelength, ridge power (power is the rate of transfer of energy), ridgeenergy, ridge energy density (energy density is the amount of energy perunit area of the transform surface, which may be thought of as a surfacediscretized into a patchwork of tiles each of which has an associatedenergy), ridge amplitude, ridge amplitude variability, ridge scalevariability, ridge consistency, product of ridge strength and ridgelength, the intrinsic or characteristic scale for the ridge. In someembodiments, the ridges 520 and 522 may be characterized in terms ofproducts of or weighted sums of these parameters (step 526). In otherembodiments, ridges 520 and 522 may be characterized in terms of onlyone of these parameters (step 526). Based on the calculated/derivedridge parameters, at step 528, a ridge density distribution or ridgedensity distribution function, e.g., ridge parameters or a weighting ofridge parameters as a function of scale, may be calculated (step 528).For example, the total length of ridges as a function of scale, or thetotal energy of ridges as a function of scale. In preferred embodiments,respiration rate 516 may be determined as being the scale within therespiration scale-range corresponding to the maximum value of the ridgedensity distribution (step 530).

Ridge density distribution (RDD) as generated, for example, in step 528of FIG. 5 c, may be calculated in any suitable manner. For example,ridge density distribution may be computed as a histogram of ridges of acertain length for a given scale (see for example, Graph 616 in FIG. 6or Graph 1060 in FIG. 10). In other embodiments, ridge densitydistribution may be computed as a histogram of ridges of a certainstrength for a given scale. In some embodiments, the ridge parametersmay be weighted using any suitable weighting. Such a weighting may beachieved by any suitable ridge density distribution (RDD).

In some embodiments, an RDD includes an assignment of weightings, or amapping of ridge parameters to weighted ridge parameters, based on a setof weighting coefficients for each ridge in relation to neighboring (inthe scale axis) ridges, see, e.g., the discussion accompanying FIG. 9.The goal in such weighting may be to reduce the relative importance ofsome ridge components, which may be useful when attempting to removeridge components which are not of interest. In other embodiments, somecharacterizing parameters or weighting parameters are considered moreimportant than others, e.g., length, strength-length product, or anyother suitable parameter, may be considered to be of more significancethan other parameters.

In embodiments, the weighting of a ridge may be decreased based oncharacterizing parameter values. For example, a ridge with highamplitude or scale variation may cause a ridge to have a lower weightingthan one with low amplitude or scale variation. Ridges may also beweighted based on a comparison of characterizing parameters of the ridgebeing weighted relative to the characterizing parameter(s) of otherridges. For example, a first ridge having parameters that are similar tothe parameters of second ridge (e.g., scale, length, and amplitude) maycause the weighting of the first ridge to increase. This may causerespiration ridges from different scalograms to have a reinforcing ormultiplying affect on each other. In some embodiments, the respirationrate that is selected is the scale at the point with the maximum RDDvalue i.e. respiration rate is the scale within the respirationscale-range at which the largest density of ridges occurs.

Turning now to FIG. 6, an illustration of how process 500 of FIG. 5 maybe applied to a PPG signal to determine respiration rate is shown. Graph602 shows a PPG signal with a segment which is under analysis, and aclose-up of the modulation of the PPG signal below this segment. Abreath position verification signal in raw form and processed formcorresponding to this PPG signal appears in Graph 604. Graph 606 showsthe primary scalogram of a portion of the red segment of the PPG signalsegment being analyzed. This scalogram shows several dominant ridgefeatures, including, but not limited to, pulse ridges (corresponding toheart rate) in the pulse scale-range and respiration ridges in therespiration scale-range. In preferred embodiments, the pulse ridges maybe extracted (see, e.g., extracted pulse ridges 509 in process 500 ofFIG. 5 a). Graphs 608, 610, and 612 show features extracted from theprimary scalogram that may be used to generate secondary scalograms.Specifically, graph 608 shows scale modulation of the extracted pulseridge in Graph 606 along the ridge loci. Graph 610 shows amplitudemodulation of the extracted pulse ridge in Graph 606 along the ridgeloci. Graph 612 shows off-ridge amplitude modulation of the extractedpulse ridge in Graph 606 along the ridge loci, Graphs 614 and 616 showhow respiration rate may be determined from the RDD, as explained inmore detail in relation to FIGS. 7-10. In particular, the ridgesobtained from the primary and secondary scalograms in the respirationscale-range may be characterized in terms of their length, Graph 616shows a plot of ridge length versus scale, with each point representinga different ridge at a specific scale. In some embodiments, therespiration rate is selected as the scale at the point with the highestRDD value i.e. respiration rate is the scale within the respirationscale-range at which the largest density of ridges occurs. In someembodiments, the ridge density distribution may be filtered, e.g., witha notch filter, to remove undesired scale-ranges e.g., ranges of scalecorresponding to pulse rate. For example, in FIG. 6, respiration rate,i.e., 0.315 Hz, is determined by selecting the scale at which the ridgedistribution density is maximum in Graph 616.

In some embodiments, the RDD may include an assignment of weightingsaccording to a set of coefficients for each point in relation toneighboring points. For instance, points which are grouped together mayreceive a higher weighting than points which lie apart from groups. Tothis end, closer-grouped points re-enforce each other, while pointsspaced far apart or isolated points do not get re-enforced. For example,the RDD in graph 616 in FIG. 6 may be based in part on relationshipsbetween points in graph 614 in FIG. 6. Such a weighting may beperformed, among others, using a nearest neighbors analysis method.

FIG. 7 shows another exemplary respiration rate determination accordingto an embodiment. A physiological signal 702, e.g., a PPG signal, may beanalyzed and processed as part of input data 700 to produce one or moreprimary scalograms 710. S, A, and O components 704, 706, and 708,respectively, may be derived from the primary scalogram and used togenerate secondary scalograms. The S, A, and O components are displayedin composite graph 720. Ridges may be identified in one, several, or allof the generated scalograms. The identified ridges may be shown, forexample, in graph 740, which plots normalized ridged length against ascale parameter of ridges. Graph 740 also illustrates the use of a notchfilter 726 to remove undesired scales in the ridge length-frequencyplot. The scales removed using notch filter 726 may be identified usingthe filtering techniques discussed above in relation to FIG. 6.

Graph 760 in FIG. 7 is a plot of the Ridge Density Distribution (RDD)versus scale, according to an embodiment. The RDD value for a ridge maybe its weighting based on one or more ridge parameters or otherweighting parameters. In some embodiments, the RDD may be based on adecision tree in which a weighted branching is used. This weightedbranching may be based on, among others, an inter-ridge relationshipbetween ridge components (e.g., the degree of cohesion between ridges,the degree of correlation between ridges, or any other suitableinter-ridge relationship) and parameters characterizing the ridgesthemselves (e.g., the start and end positions of the ridges, the ridgelengths, variance of ridge energy, ridge entropy, or any other suitableparameter). In an embodiment, the ridge having the highest RDD weightingmay be representative of respiration rate. As shown in graph 760 in FIG.7, the ridge having the highest RDD weighting (i.e., RDD 722) maycorrelate to a respiration rate of approximately 13 breaths per minute.The respiration rate may be determined based on the characteristicfrequency of the scale of the highest weighted ridge or using any othersuitable mapping.

As shown in graph 760, another RDD 724 is shown to be close to RDD 722,according to an embodiment. This may occur when two or more continuousrespiration ridges are identified on two or more scalograms. Whenmultiple ridges are determined to have high weightings, the highestweighted ridge may be selected for determining respiration rate.Alternatively, a weighted average, median, or other suitable measurementof the two or more highest weighted ridges may be used to determinerespiration rate or any other suitable parameter.

FIG. 8 is an illustration of scalograms of a PPG signal that may beanalyzed according to an illustrative embodiment. The top portion ofFIG. 8 illustrates a primary scalogram 810 of a PPG signal in which arespiration ridge 830 is highlighted. This ridge corresponds to arespiration frequency of 0.26 Hz. Also shown in the primary scalogram810 of FIG. 8 is a pulse ridge 850 corresponding to heart rate. Theprimary scalogram 810 is one that may be computed at step 504 of process500 in FIG. 5 a. Ridges such as ridge 830 or ridge 850 which are ridgesin the primary scalogram may be referred to as B components.

The bottom portion of FIG. 8 corresponds to a secondary scalogram 820that may be obtained by computing the continuous wavelet transform of asignal derived from primary scalogram 810. The secondary scalogram 820is one that may be computed at step 506 of process 500 in FIG. 5 a.Continuous wavelet transforms of the O-mapping, S-mapping, andA-mapping, may be computed as described above in relation to FIG. 5 b,and these transforms may be referred to as secondary scalograms.Although the secondary scalograms discussed herein correspond to theA-mapping, S-mapping, and O-mapping, any other suitable secondaryscalogram may be used. The respiration ridge 840 in secondary scalogram820 corresponds to a respiration frequency of 0.29 Hz. As shown in FIG.8, secondary scalogram 820 may not have a ridge corresponding to heartrate when it is derived from the pulse ridge.

In some embodiments, ridges may be parameterized in terms of one or morequantities which characterize the ridge, as illustrated in graph 614 inFIG. 6 or in FIG. 9, or in terms of quantities or variables whichcharacterize the relationship between two or more ridges. In oneembodiment, the ridges may be represented by one quantity. For example,a ridge may be represented by its mean amplitude. In FIG. 9, such aparameterization may be carried out for ridges A and B in scalogram 900based on maximum amplitude (parameterization 910) and ridge length(parameterization 920). Also, in FIG. 6, such a parameterization may becarried out based on ridge length in Graph 614. Note that differentparameterizations may characterize the ridge components in differentways. For example, the relative strength of ridge A or ridge B mayappear to be different depending on which parameterization is used. See,for example, the relative properties of ridges A and B inparameterizations 910 and 920, respectively, in FIG. 9.

In some embodiments, before calculating parameters for the ridges oreven before identifying the ridges, filtering may be performed to removeundesired information as described in relation to FIG. 5 a-c above. Forexample, it is possible that any of the scalograms described herein maysuffer from a high degree of cohesion, i.e., a high degree of time-scaleoverlap between ridge components. Inasmuch as this overlap may obscuredesired information, e.g., a ridge corresponding to respiration rate,from undesired information, e.g., noise or movement artifacts, or aridge corresponding to the pulse rate, the filters described in relationto FIGS. 5 a-c may be employed to remove the undesired information,e.g., identify bands or features that may occur due to artifacts, noise,or other phenomena. The filtering process may, for example, generate amask to ignore regions of the scalogram. Alternatively, the filteringprocess may zero-out the amplitude in regions of the scalogram. Thefiltering process may use techniques described in Addison et al. U.S.patent application Ser. No. ______, (Attorney Docket No. H-RM-01195-01(COV-01-01), filed Oct. 3, 2008, entitled “Methods and Systems forDiscriminating Bands in Scalograms,” which is incorporated by referenceherein in its entirety. In the discussion herein, it may be assumed thatthat the filtering process has been performed. However, the discussionis also applicable if no filtering has been performed.

The type of wavelet used to compute a scalogram may affect the relativeproperties of a parameterized ridge and its corresponding band asillustrated in an embodiment in FIG. 10. In FIG. 10, a technique isshown that may be used to minimize the effect of “rabbit ears” accordingto an embodiment. Rabbit ears are a phenomena that may occur on bandswithin a scalogram, mainly due to differences in the temporal resolutionof the wavelets used to obtain the scalogram. In particular, scalogramscreated by computing continuous wavelet transforms of the signal atdifferent temporal resolutions, e.g., a low-temporal wavelet (i.e., amore oscillatory wavelet) may be used to compute one scalogram of thesignal, while a high-temporal wavelet (i.e., a less oscillatory wavelet)may be used to compute another scalogram of the signal, may result inremarkably different ridges. In FIG. 10, a physiological signal 1002,e.g., a PPG signal may be used to compute two scalograms: scalogram I1004 and scalogram II 1006. In scalogram 1004, a low temporal resolutionwavelet may be used, which may cause relatively large rabbit ears tooccur. The rabbit ears may connect to create a ridge 1010 spaced apartfrom the ridge of the band (e.g., respiration band) from which theyextend. The ridge running through the rabbit ears may not be a ridge ofinterest. In scalogram 1006, a higher temporal resolution wavelet may beused to generate a scalogram where effects of the rabbit ears may beminimized. As shown in FIG. 10, rabbit ears ridge 1010 from scalogram1004 may be broken into three ridge segments 1022, 1024, and 1026 when ahigher temporal wavelet is used in scalogram 1006. Accordingly, whenridges identified from 1004 and 1006 are analyzed and weighted, theridges corresponding to the bands in scalograms 1004 and 1006, which aresimilar to each other, may reinforce each other and be weighted higherthan the rabbit ears ridges, which may be of different sizes andamplitudes between the two scalograms. However, it should be noted thatusing wavelets of too high of a resolution may also cause the ridge ofthe respiration band or other bands of interest to break into separateridge segments, which may not be desirable.

The foregoing is merely illustrative of the principles of thisdisclosure and various modifications can be made by those skilled in theart without departing from the scope and spirit of the disclosure. Thefollowing numbered paragraphs may also describe various aspects of thisdisclosure.

1. A method comprising: transforming a signal based at least in part awavelet transform to generate a transformed signal, generating a firstwavelet scalogram based at least in part on the transformed signal,detecting ridges within a region of the first wavelet scalogram,determining one or more parameters for the detected ridges, determininga ridge density distribution function based at least in part on the oneor more parameters, and selecting a ridge based at least in part on theridge having the scale corresponding to a maximum value of the ridgedensity distribution function.
 2. The method of claim 1, wherein thesignal is a photoplesthymographic signal.
 3. The method of claim 1,further comprising filtering the first wavelet scalogram.
 4. The methodof claim 1, further comprising generating a second wavelet scalogrambased at least in part on a signal derived from the first waveletscalogram and detecting ridges within a region of the second waveletscalogram.
 5. The method of claim 1, wherein the parameters of thedetected ridges comprise ridge power, ridge energy, ridge energydensity, ridge amplitude variability, ridge scale variability, ridgeconsistency, intrinsic scale, ridge length, maximum ridge amplitude,standard deviation of intrinsic scale, standard deviation of amplitude,mean scale, median scale, mean amplitude, median amplitude, and/orstrength-length product.
 6. The method of claim 1, further comprisingdetermining a physiological parameter based at least in part on theselected ridge.
 7. The method of claim 6, wherein the physiologicalparameter comprises respiration rate.
 8. A device for determining aphysiological parameter, the device comprising: a processor capable of:transforming an input signal at least in part using a wavelet transformto generate a transformed signal, generating a first wavelet scalogrambased at least in part on the transformed signal, detecting ridgeswithin a region of the first wavelet scalogram, determining one or moreparameters for the detected ridges, determining a ridge densitydistribution function based at least in part on the one or moreparameters, and selecting a ridge based at least in part on the ridgehaving the scale corresponding to a maximum value of the ridge densitydistribution function.
 9. The device of claim 8, wherein the signal is aphotoplesthymographic signal.
 10. The device of claim 8, wherein theprocessor is capable of filtering the first wavelet scalogram.
 11. Thedevice of claim 8, wherein the processor is further configured togenerate a second wavelet scalogram based at least in part on a signalderived from the first wavelet scalogram and detect ridges within aregion of the second wavelet scalogram.
 12. The device of claim 8,wherein the parameters of the detected ridges comprise ridge power,ridge energy, ridge energy density, ridge amplitude variability, ridgescale variability, ridge consistency, intrinsic scale, ridge length,maximum ridge amplitude, standard deviation of intrinsic scale, standarddeviation of amplitude, mean scale, median scale, mean amplitude, medianamplitude, and/or strength-length product.
 13. The device of claim 8,further comprising a display for displaying a physiological parameter,and wherein the processor is further configured to determine thephysiological parameter based at least in part on the selected ridge.14. The device of claim 8, wherein the physiological parameter comprisesrespiration rate.
 15. A computer-readable medium comprisingcomputer-executable instructions which, if executed by a processor,cause the processor to carry out a method for determining aphysiological parameter from one or more scalograms of a signalcomprising: transforming an input signal at least in part using awavelet transform to generate a transformed signal, generating a firstwavelet scalogram based at least in part on the transformed signal,detecting ridges within a region of the first wavelet scalogram,determining one or more parameters for the detected ridges, determininga ridge density distribution function based at least in part on the oneor more parameters, and selecting a ridge based at least in part on theridge having the scale corresponding to a maximum value of the ridgedensity distribution function.
 16. The computer-readable medium of claim15, wherein the signal is a photoplesthymographic signal.
 17. Thecomputer-readable medium of claim 15, further comprisingcomputer-executable instructions which, if executed by a processor,cause the processor to generate a second wavelet scalogram based atleast in part on a signal derived from the first wavelet scalogram anddetect ridges within a region of the second wavelet scalogram.
 18. Thecomputer-readable medium of claim 15, wherein the parameters of thedetected ridges comprise ridge power, ridge energy, ridge energydensity, ridge amplitude variability, ridge scale variability, ridgeconsistency, intrinsic scale, ridge length, maximum ridge amplitude,standard deviation of intrinsic scale, standard deviation of amplitude,mean scale, median scale, mean amplitude, median amplitude, and/orstrength-length product.
 19. The computer-readable medium of claim 15,further comprising computer-executable instructions which, if executedby a processor, cause the processor to determine a physiologicalparameter based on the selected ridge.
 20. The computer-readable mediumof claim 19, wherein the physiological parameter comprises respirationrate.